MODIFICATION OF NEILL'S EQUATION FOR STORM‐TIDE DESIGN FLOW ANALYSIS1

ABSTRACT: Design of bridges spanning tidal estuaries or bays requires an estimate of peak tidal flow. One common approach to estimating these flows (Neill's method) uses a first‐order approximation of uniform water surface rise in the water body. For larger water bodies, the assumptions of this method are decreasingly valid. This study develops a simple modification that accounts for the spatial variability in the response of tidal waterways to storm surge flows. The peak tidal flow predicted by Neill's equation is compared to the peak flow determined by numerical simulation of estuaries with simple geometries, ranging from 1 to 25 km in length, using the U.S. Army Corps of Engineers one‐dimensional unsteady flow model, UNET. Results indicate that, under certain conditions, it may be appropriate to apply a correction factor to the peak discharge and peak velocity predicted by Neill's method. An algorithm, developed by nonlinear regression, is presented for computing correction factors based on estuary length, shape, mean depth, and storm‐tide characteristics. The results should permit the design of more reliable, cost‐effective structures by providing more realistic estimates of the potential for bridge scour in tidal waterways, especially when a full solution of the unsteady flow equations is impractical.     

SIMULATING THREE-DIMENSIONAL GROUND WATER RESPONSE IN A SMALL MOUNTAINOUS WATERSHED1

ABSTRACT: Snowmelt from deep mountainous snowpacks is seldom rapid enough to exceed infiltration rates; thus, the source of streamflow in many mountainous watersheds is snowmelt recharge through shallow ground water systems. The hydrologic response and interaction between surface and sub-surface flow processes in these watersheds, which is controlled by basin structure, the spatial distribution of snowmelt, and the hydrogeology of the subsurface, are not well understood. The purpose of this study was to test a three-dimensional ground water model using simulated snowmelt input to simulate ground water response to spatially distributed snowmelt on the Upper Sheep Creek Watershed located within the Reynolds Creek Experimental Watershed in Southwestern Idaho. The model was used to characterize the mountainous aquifer and to delineate the subsurface flow mechanisms. Difficulty in finding a reasonable combination of grid spacing and time stepping within the model was encountered due to convergence problems with the Picard solution to the non-linear variably saturated ground water flow equations. Simulation results indicated that flow may be either unconfined or confined depending on inflow rate and hydrogeologic conditions in the watershed. The flow mechanism had a much faster response time when confined flow occurred. Response to snowmelt from a snow drift approximately 90 m away took only a few hours when flow was confined. Simulated results showed good agreement with piezometer measurements both in magnitude and timing; however, convergence problems with the Picard solution limited applicability of the model.     

CRITICAL EVALUATION OF CERTAIN METHODS OF UNSTEADY GROUNDWATER HYDRAULICS1

The basic theories and fundamental assumptions usually employed in the solution of unsteady groundwater flow problems are reviewed critically. The best known method of analysis for such problems is based on the Dupuit-Forchheimer approximation and leads to a nonlinear parabolic differential equation which is generally solved by linearization or numerical methods. The accuracy of the solution to this equation can be improved by use of a different approach which does not employ the Dupuit Forchheimer assumption, but rather is based on a semi-numerical solution of the Laplace equation for quasi-steady conditions. The actual unsteady process is replaced by a sequence of steady-state conditions, and it is assumed that the actual unsteady flow characteristics during a short time interval can be approximated by those associated with “average” steady state flow. The Laplace equation is solved by a semi-discretization method according to which the horizontal coordinate is divided into subintervals, while the vertical coordinate is maintained continuous. The proposed method is applied to a typical tile drainage problem, and, based on a comparison of calculated results with experimental data, the method is evaluated and practical conclusions regarding its applicability are advanced.     

VELOCITY EQUATION FOR WATER QUALITY MODELING IN GEORGIA1

ABSTRACT: Tabletop water quality modeling still plays an important role in the water pollution control activities of the Georgia Environmental Protection Division. Tabletop models are those developed with out the aid of extensive field data. One important component of GEORGIA DOSAG, our basic water quality model, is the equation used to predict flow through velocity. However, Georgia is characterized by wide physiographic diversity which reduces the effectiveness of uncalibrated velocity equations. Using 15 years of accumulated time-of-travel studies, a series of empirical velocity equations were developed and calibrated to various physiographic conditions in Georgia. Equations are available for each major soil province and for three stream flow ranges within each province - Q<100 cfs, 100<Q<1000 cfs, and Q>1000 cfs. Now, in the absence of extensive field data, we have data based velocity equations which can be tailored to each site under study.     

MATHEMATICAL ANALYSIS OF ARTIFICIAL RECHARGE FROM BASINS1

ABSTRACT: One of the most common methods of artificial recharge to the ground water is from basins. In this paper, seven analytical solutions that describe artificial recharge from basins are presented. Most of these solutions are derived by directly solving the general partial differential equation for ground water flow. The solutions differ in that they use different boundary conditions, basin shapes, and consider the nonlinearity of the artificial recharge problem differently. Use of each analytical solution is demonstrated in this paper by application to an example problem. A comparison of each analytical solution presented in this paper was made to give suggestions on their use, their ease of implementation, and their relative agreement. Although no attempt is made in the paper to conclude which analytical solution is best for all problems, some general conclusions can be stated on the applicability of the various analytical solutions. Of the analytical solutions presented in this paper, Glovers and Hantush's solutions for rectangular recharge basins are highly recommended. Baumanns solution for a circular basin also gave fairly reliable results and is very easy to evaluate numerically.     

DYNAMIC RESPONSE OF AQUIFER SYSTEMS TO LOCALIZED RECHARGE1

ABSTRACT. The response of stream-unconfined aquifer systems to localized recharge is investigated by means of a two-dimensional finite element model. A variational approach is used in conjunction with the finite element method to solve the ground water flow equation. Linear approximated triangular elements are used to calculate the hydraulic head distribution in the flow region. The Crank-Nicholson centered scheme of numerical integration is employed to approximate the time derivative in the flow equation. A computer program is developed to calculate the hydraulic head distribution in the flow region. Solutions provided by the finite element model should prove useful in the evaluation of quantitative and qualitative changes in aquifer systems due to natural or artificial recharge. In addition, they should prove useful in the study of irrigation and drainage problems.     

GROUND WATER DROUGHT MANAGEMENT BY A FEEDFORWARD CONTROL METHOD1

ABSTRACT: Management of a regional ground water system to mitigate drought problems at the multi‐layered aquifer system in Collier County, Florida, is the main topic. This paper developed a feedforward control system that consists of system and control equations. The system equation, which forecasts ground water levels using the current measurements, was built based on the Kalman filter algorithm associated with a stochastic time series model. The role of the control equation is to estimate the pumping reduction rate during an anticipated drought. The control equation was built based on the empirical relationship between the change in ground water levels and the corresponding pumping requirement. The control system starts with forecasting one‐month‐ahead ground water head at each control point. The forecasted head is in turn used to calculate the deviation of ground water heads from the monthly target specified by a 2‐in‐10‐year frequency. When the forecasted water level is lower than the target, the control system computes spatially‐varied pumping reduction rates as a recommendation for ground water users. The proposed control system was tested using hypothetical droughts. The simulation result revealed that the estimated pumping reduction rates are highly variable in space, strongly supporting the idea of spatial forecasting and controlling of ground water levels as opposed to a lumped water use restriction method used previously in the model area.     

OPTIMIZATION OF WATER ALLOCATION DECISIONS AFFECTING ESTUARINE ECOLOGY1

ABSTRACT .The problem analyzed in this paper is how to allocate optimally the available surface water in a river system among those who compete for its use, while acknowledging explicitly that for coastal states the ecology of bays and estuaries must be numbered among the competitors. The objective is to maximize the benefit resulting from water use while satisfying a set of constraints on flow. Benefit is assumed to be a function of the amount of water used and the time period in which the water is used. A mathematical model of this problem is shown to fit the format of the minimum cost circulation network flow problem. The Out-of-Kilter algorithm of D. R. Fulkerson is proposed as a solution technique. Sensitivity analysis on the input data is described as a means of determining the minimum economic benefit required to justify the allocation of a given volume of water needed to sustain the ecology of an estuary.     

Analysis of the Effect of the Beavers‐Joseph Interface Condition on Flow in Karst Conduits1

Li, Guangquan, Yuan Cheng, and Bei Zhao, 2012. Analysis of the Effect of the Beavers‐Joseph Interface Condition on Flow in Karst Conduits. Journal of the American Water Resources Association (JAWRA) 1‐8. DOI: 10.1111/j.1752‐1688.2012.00683.x Abstract: In this study, we derive an approximate analytic solution for the distribution of flow velocity in a cylindrical conduit and the surrounding media, and analyze the effect of differing parameters (e.g., conduit radius) on the velocity of conduit flow. The solution is then employed to estimate the thickness of the boundary layer inside the media. The results reveal that when conduit radius is large, the Beavers‐Joseph condition has only a minor effect on the velocity of conduit flow (such that the nonslip condition on the conduit wall still works pretty well), and the boundary layer is so thin that the wall can still be treated as the interface between fast water in the conduit and slow water in the media. The solution indicates that the velocity of conduit flow is the superposition of the velocity profile in the nonslip situation onto the slip velocity on the wall. Our study theoretically shows that the coupled continuum pipe flow model in MODFLOW‐2005 constructed by the U.S. Geological Survey is reasonable in that there is no need to consider the Beavers‐Joseph condition when simulating flow in karst conduits. The role of the boundary layer in transport and its effect on the hyporheic zone is not clear, which is a suitable topic for future study.     

A NEW METHOD FOR ESTIMATING PRODUCTIVITY IN STANDING WATERS USING FREE OXYGEN MEASUREMENTS1

ABSTRACT: Continuous measures of net productivity at discrete depths in standing waters may be obtained using diurnal free oxygen measurements and estimates of the vertical mixing. If oxygen concentration and vertical mixing are known in a laterally homogeneous water body, the only unknown term in the oxygen mass-balance equation is net productivity. If this is represented by a Fourier series, the equation may be solved and Fourier coefficients selected so that the sum of square errors between the oxygen measurements and predictions of the equation is minimized; the Fourier series then describes the diurnal variation of net productivity.     

WAVE INDUCED FLOW AND TRANSPORT IN SEDIMENT BEDS1

ABSTRACT: The fate of contaminants in large water bodies is highly influenced by the transfer of flow and solutes across the water sediment interface. In this paper, an analytical model is presented where flow in both sediment bed and open channel is coupled at the interface through a boundary layer occupying the upper part of the sediment bed. The presence of this layer allows not only the capture of the inertia effects through a drag term in the generalized Darcy's equation, but also the specification of different soil parameters for the two porous zones. The flow is advective and driven by wave action along the water surface. The resulting system is solved for the pressure and flux in each sediment layer. The generated transport velocity fields are linked to a random walk simulation that is used to examine the trajectories of solute particles. Comparison of these trajectories against experimental tracer tests suggests a pattern very similar to the one attributed to the presence of surface mounds. The results clearly show the significance of the boundary layer and the drag term for soil with high permeability and the impact of both the thickness of the boundary layer and the length of the gravity wave relative to the depth of the water channel on the transport and exchange across the interface. The paper also examines the sensitivity of the mass exchange to the permeability of the two porous zones.     

PARALLEL DRAINS FROM THE LAPLACE STANDPOINT1

Where natural drainage is inadequate for keeping the water table below the root zone of the crops being grown, drains are often employed to control water table levels. Such drains are commonly installed in parallel lines at depths and spacings adapted to the needs of the area. Formulas used for determining drain spacings are generally based upon Dupuit-Forchheimer concepts. These developments postulate a saturated, permeable aquifer underlying the irrigated area and an impermeable barrier underlying the aquifer. The basic differential equation expresses the requirement that the flow out through the sides of a vertical column of infinitesmal cross sectional area must be supplied by a corresponding drop of the water table at the top of the column. If variations of transmissivity due to variations of water table level are taken into account the second order differential equation obtained is nonlinear. To avoid the mathematical difficulties posed by this nonlinearity it is customary to neglect the effects of changes of transmissivity due to changes of water table levels. This imposes a restriction that the formulas derived from these linearized differential equations suffer a loss of accuracy if the change of water table levels becomes a considerable portion of the initial saturated depth. Offsetting these difficulties is the tactical advantage that the linearized differential equations are of types long studied in older developments concerned with conduction of heat in solids. The advantages conferred by the possibilities for exploiting the results of investigations in the older discipline are many. An alternative approach is based upon a requirement that there can be no accumulation of water in any elementary cubical volume located in the zone of complete saturation below the water table. The differential equation obtained on this basis, if the aquifer is homogeneous and isotropic, is the one which bears the name of Laplace. It will be the purpose of this paper to explore the possibilities afforded by this approach for evaluating the flow to parallel drains and to compare the results with those obtainable by the Dupuit-Forchheimer method.     

Effect of Snow Cover Conditions on the Hydrologic Regime: Case Study in a Pluvial‐Nival Watershed,Japan1

Abstract: Hydrologic monitoring in a small forested and mountainous headwater basin in Niigata Prefecture has been undertaken since 2000. An important characteristic of the basin is that the hydrologic regime contains pluvial elements year‐round, including rain‐on‐snow, in addition to spring snowmelt. We evaluated the effect of different snow cover conditions on the hydrologic regime by analyzing observed data in conjunction with model simulations of the snowpack. A degree‐day snow model is presented and applied to the study basin to enable estimation of the basin average snow water equivalent using air temperature at three representative elevations. Analysis of hydrological time series data and master recession curves showed that flow during the snowmelt season was generated by a combination of ground water flow having a recession constant of 0.018/day and diurnal melt water flow having a recession constant of 0.015/hour. Daily flows during the winter/snowmelt season showed greater persistence than daily flows during the warm season. The seasonal water balance indicated that the ratio of runoff to precipitation during the cold season (December to May) was about 90% every year. Seasonal snowpack plays an important role in defining the hydrologic regime, with winter precipitation and snowmelt runoff contributing about 65% of the annual runoff. The timing of the snowmelt season, indicated by the date of occurrence of the first significant snowmelt event, was correlated with the occurrence of low flow events. Model simulations showed that basin average snow water equivalent reached a peak around mid‐February to mid‐March, although further validation of the model is required at high elevation sites.     

Effects of warm water inflows on the dispersion of pollutants in small reservoirs

The effects of the warm water discharged by a nuclear power plant (NPP) into a small reservoir are studied. A case study is presented (José Cabrera NPP-Zorita Hidráulica Reservoir) with experimental data of the reservoir stratification and predicted data of the dispersion of radioactive pollutants from operative or accidental releases. The vertical and longitudinal temperature profiles, electrical conductivity and transparency of the reservoir water were measured for an annual cycle. The results indicate that the continuous warm water discharge from the NPP causes permanent and artificial reservoir stratification. The stratification is significant within 1500 m upstream and 1000 m downstream from the warm water outfall. The pollutant dispersion has been predicted by using a flow model based on N(T) perfect-mixing compartments in series with feedback. The model parameter, N(T), is calculated from the longitudinal diffusion coefficient. The prediction of pollutant dispersion by means of this model shows that the stratification slows down the vertical mixing in the whole water body, and reduces the reservoir volume that is effective for the dilution and dispersion of pollutants. This means that, in the case of a radioactive pollutant release, the reservoir radioactivity level could increase significantly.     

PREDICTING THE SUMMER TEMPERATURE OF SMALL STREAMS IN SOUTHWESTERN WISCONSIN1

ABSTRACT: One of the biggest challenges in managing cold water streams in the Midwest is understanding how stream temperature is controlled by the complex interactions among meteorologic processes, channel geometry, and ground water inflow. Inflow of cold ground water, shade provided by riparian vegetation, and channel width are the most important factors controlling summer stream temperatures. A simple screening model was used to quantitatively evaluate the importance of these factors and guide management decisions. The model uses an analytical solution to the heat transport equation to predict steady‐state temperature throughout a stream reach. The model matches field data from four streams in southwestern Wisconsin quite well (typically within 1°C) and helps explain the observed warming and cooling trends along each stream reach. The distribution of ground water inflow throughout a stream reach has an important influence on stream temperature, and springs are especially effective at providing thermal refuge for fish. Although simple, this model provides insight into the importance of ground water and the impact different management strategies, such as planting trees to increase shade, may have on summer stream temperature.     

A Semianalytical Solution for Residual Drawdown at a Finite Diameter Well in a Confined Aquifer

After the end of pumping the water level in the observation well starts to recover and the reduced drawdown during the recovery period is named as the residual drawdown. Traditional approaches in analyzing the data of residual drawdown for estimating the aquifer hydraulic parameters are mostly based on the application of superposition principle and Theis equation. In addition, the effect of wellbore storage is commonly ignored in the evaluation even if the test well has a finite diameter. In this article, we develop a mathematical model for describing the residual drawdown with considering the wellbore storage effect and the existing drawdown distribution produced by the pumping part of the test. The Laplace‐domain solution of the model is derived using the Laplace transform technique and the time‐domain result is inverted based on the Stehfest algorithm. This new solution shows that the residual drawdown associated with the boundary and initial conditions are related to the well drawdown and the aquifer drawdown, respectively. The well residual drawdown will be overestimated by the Theis residual drawdown solution in the early recovery part if neglecting the wellbore storage. On the other hand, the Theis residual drawdown solution can be used to approximate the present residual drawdown solution in the late recovery part of the test.     

OPTIMAL ESTIMATION OF CONTAMINANT TRANSPORT IN GROUND WATER1

ABSTRACT: Finite element and finite difference representations of the convective-dispersive equation have been widely used in determining contaminant transport in ground water. Due to inherent uncertainties of the transport process, those representations are inexact and contain errors. Errors in field measurements are unavoidable. By combining a numerical model, a measurement equation, and the Kalman filter, optimal estimates of the state variable (contaminant concentration) can be obtained. This paper describes the algorithm and gives a numerical example of contaminant transport in a two-dimensional ground water flow. The results show significant improvement in the estimated concentration distribution by using the filtering technique.     

Water quality modeling to determine minimum instream flow for fish survival in tidal rivers

The Hsintien Stream is one of the major branches of the Danshuei River system, which runs through the metropolitan capital city of Taipei, Taiwan and receives a large amount of wastewater. The dissolved oxygen concentration is generally low in the tidal portion of the Hsintien Stream. Hypoxia/anoxia occurs often, particularly during the low-flow period when the Feitsui Reservoir, Chingtan Dam and Chihtan Dam impound the freshwater for municipal water supply. Fish kills happen from time to time. This paper describes the application of a numerical hydrodynamic and water quality model to the Danshuei River system, with special attention to the tidal portion of the Hsintien Stream. The model is recalibrated with the prototype conditions of the year 2000. The hydrodynamic portion of the model is recalibrated with measured surface elevation and velocity at various stations in the river system. The water quality portion of the model is recalibrated with respect to the field data provided by Taiwan EPA. The input data of point and nonpoint sources are also estimated. The model simulates the concentrations of various forms of nutrients, CBOD and dissolved oxygen. A series of sensitivity runs was conducted to investigate the effects of point source loadings and river flow on the DO level in the river. It is demonstrated that the augmentation of river flow has as much effect on raising DO level as the reduction of point source loadings. The completion of the Taipei sewer project is expected to reduce the point source loadings by at least 75%. Under these reduced loadings, if the daily instream flow is maintained above the monthly Q75 flow throughout the year, the minimum DO concentration in the river would not fall below 1mg/L, which is the suffocation level for most fish species in the Hsintien Stream. (Q75 is the flow which is equaled or exceeded 75% of the days in the month.) The Feitsui Reservoir, Chingtan Dam and Chihtan Dam may impound water during the high flow periods and release freshwater to maintain the flow at the Q75 value in the Hsintien Stream during the drought periods.     

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION1

ABSTRACT: Operation of a storage‐based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long‐term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent.